Optimal flop cbetting - part 2

7/27/2019 Optimal flop cbetting - part 2

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. Introduction

is is Part 2 of the series "C-Betting in NLHE 6-max" where we take a closer look at flop c-bet

NLHE 6max. In Part 1 we looked at c-betting heads-up and out of position as the preflop raise

e studied c-betting with "air" (worthless hands) on two example flops:

ordinated flop

y flop

e assumed that the raiser had opened our standard 25% CO range:

+

s+ A9o+s+ KQo

s+ QTo+

s+ JTo

s+

s+

s

s

s

6 combos

%

hile the flatter used our standard ~10% "IP flat list", defined in the article series "Optimal 3/4/

ting in NLHE 6-max", and given in the summary document below:


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wnload link (right-click and choose "Save as ..."): IP_3-bet_summary.doc

e wanted to find out whether or not c-betting any two cards was profitable on these two flop

tures, against this preflop flatting range. First we let the flatter defend optimally against the c-b

both flop textures. When he does, the preflop raiser can (per definition) not profit from c-betti

y two cards as a bluff. The flatter defends just enough to prevent it (1/(1 + 0.75) =57% defense

c-bet is 0.75 x pot).
http://dev.donkr.com/articles/bugs/v2/c-bet/c-bet-2/IP_3-bet_summary.doc


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xt, we let the flatter deviate from optimal flop play. We let him play closer to the way a typica

ak-tight opponent plays, namely folding too much on certain flop textures and not defending

gressively enough. More specifically, we gave him the following restrictions on the flop:

1. He is unwilling to bluff raise

2. He is unwilling to call c-bets with pairs lower than two of the board cards (e.g. he will

77 and lower pairs on a A 8 2 flop).

3. He is unwilling to float naked overcards or naked gutshots without additional draws

other words, we assumed that the flatter would play straightforward against c-bets, and that he

uld see each hand as an isolated case. He does not think about defending his total range

fficiently against c-bets, but thinks only about whether or not the hand he has right now can be

yed profitably on the flop in a vacuum.

lding a lot on the flop can be better for him than calling c-bets with lots of weak hands, if he door job of stealing on later streets (you need to be willing to sometimes steal on the turn and riv

u are floating a lot of weak hands on the flop). But note that if you're not willing to defend corr

the flop, you might lose money by flatting preflop. For example, if you're not willing to somet

se J9 as a bluff on a T72 flop, or float and bluff turns when checked to, you might not have a

ofitable flat preflop with this hand.

sed on the assumptions above we reached the following conclusions:

It was unprofitable for the raiser to c-bet any two cards on the coordinated example flop, e

with restrictions on the flatter's flop defense strategy

It was clearly profitable for the raiser to c-bet any two cards on the dry flop texture, when

imposed restrictions on the flatters flop defense strategy

e concluded that the preflop raiser should check and give up with his total "air" hands (like 22,

, and 76) on the very coordinated example flop. Also when the flatter defends in a weak-tightnner on the flop. Simply put, such very coordinated flops are very easy to defend correctly, an

re is nothing the preflop raiser can do about it.

wever, on the very dry flops we can c-bet all our "air" hands against an opponent who plays w

ht on the flop. If he is not willing to defend with all his pairs and some naked overcards and w

aws on dry flops, we can fire away. The reason is that very dry flops mostly miss a typical pre

tting range. So in order to defend optimally on these flops, it becomes necessary to defend wit

me very weak hands. Most players are uncomfortable doing that.


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Part 2 we'll build on the modeling we did in Part 1. There we let the preflop flatter use our

ndard ~10% "IP flat list" that we introduced in "Optimal 3/4/5-betting in NLHE 6-max - Part 2

is is a flatting range we defined as our standard range in position outside of the blinds, regard

the raiser's position.

w we'll give the flatter the option to vary his flatting range. We'll give him two more choices:

A tight ~5% flatting range

A loose ~15% flatting range

e'll repeat the modeling process from Part 1 using these two ranges, and we'll see if our

nclusions change. We'll find answers to the following questions:

Which range is easier to defend on a coordinated flop?

Which range is easier to defend on a dry flop?

Will the weak-tight restrictions we impose on the flatter's flop defense strategies be morelimiting for him with a tight range or with a loose range?

hen this work is done on the very dry and very coordinated example flops. we'll look at some m

ermediate flop textures in Part 3. This will give us more insight into how various preflop flatti

nges interact with various flop textures, and the consequences this has for the profitability of c-

uffing with any two cards.

. Assumptions about ranges

sume the following model:

Alice (100 bb) raises to 3.5 bb preflop with her standard 25% CO open range. She gets fla

by Bob (100 bb) in position

Alice c-bets 0.75 x pot on the flop, and we want to know if this is automatically profitable her with any two cards

e let Bob use 3 different preflop flatting ranges:

A tight 5% range

A medium 10% range (our standard "IP flat list")

A loose 15% range


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b's 10% "IP flat list" range was given earlier in the article. His other two options are defined

ght 5% flatting range-55

s-AJs AQo

s

combos

0%

b here chooses to 3-bet or fold his lowest pocket pairs 44-22, and then he flats his remaining p

d the best high card hands that he doesn't 3-bet for value ({QQ+,AK} are value hands for Bob

ainst Alice's 25% CO range). This is a very tight flatting range, and Bob is giving up some pro

ding hands like 44-22, ATs and QJs. On the other hand, this range should be easy to defend on

ny flops, since it's so strong.

ose 15% flatting range-22

s-A6s AQo-ATo

s+ KQo

s+

s+

s+

s+

s

s

0 combos

1%

b now flats all pairs plus a wide range of high/medium unpaired hands. The unpaired hands ar

ighted towards suited and coordinated hands that will often flop draws (while hands like ATo

pends more on flopping a decent pair).

e expect this flatting range to be harder to defend correctly postflop, since it often flops

dium/weak hands and draws. When we start out with a wide and weak range, we will often ha

defend with weak hands against a flop c-bet. If we're not willing to do that, we risk folding so

uch that the preflop raiser can exploit us by c-betting any two cards profitably.

follows that in order to flat preflop with a wide and weak range, we have to be comfortable

uffing and floating with weak hands postflop. If we're not, many of the hands we flat preflop m

unprofitable for us. This is something we want to look at in our model study.

. C-betting on coordinated flop


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e'll now build Bob's defense strategies on the coordinated example flop from Part 1 with the 3

eflop flatting ranges he has at his disposal (and the work for the 10% range was done in Part 1r each range we first estimate his optimal flop strategy. On coordinated flops, Bob's defense

nsists of:

Raising his best hands

latting his next best hands

luff raise with some weak hands in a 1 : 1 value/bluff ratio

en we build a strategy that the non-optimal version of Bob can use under the following weak-ti

trictions:





hen Bob defends optimally on the flop, Alice can't c-bet any two cards profitably per definition

hen Bob deviates from optimal play, she might be able to. She c-bets 0.75 x pot, so she can c-b

y two cards with a profit if Bob folds more than 1/(1 + 0.75) =57%.

we conclude from our analysis that the non-optimal version of Bob will defend less than 57%,

ice has an automatically profitable c-bet bluff, regardless of her cards. We can then estimate th

V of her bluff with an EV calculation.

1 Defense against c-bets with a tight 5% flatting range

this flop, 55 combos remain in Bob's 5% flatting range, as shown below:


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timal defense against a 0.75 x pot c-bet means Bob has to defend 57% of his total range, whic

7 x 55 =31 combos. Here is one way to do it:

Value raise:

{TT,55} =6 combos

Flat:

{AQ,KQs,AJ,JJ} =22 combos

Bluff raise:

{AJ,AJ,AJ,99,99,99} =6 combos

Total: 34 combos (optimal: 31)

b can easily get to the optimal defense and then some. Note that a queen high flop texture

mashes" his flatting range, since almost all of his unpaired hands contain a Q. A king high flop

uld have given him fewer pairs to use, but on the other hand a K high and coordinated flop wove given him various draws he could use.

w we restrict Bob's flop defense strategy and see what we get. A possible strategy for Bob to

der these conditions is:

Value raise:

{TT,55} =6 combos

Flat:

{AQ,KQs,AJs,JJ} =25 combos

Bluff raise:

None


b has to stretch a bit by floating AJ,AJ, and AJ that only give him overcard + gutshot combos.

unwilling to float naked overcards or naked gutshots, but he can float hands that give him a

mbination of such weak draws. AJs makes the cut.

e see that the non-optimal version of Bob manages to (barely) get to optimal defense with his ti

% flatting range on our coordinated example flop. Alice can not c-bet any two cards profitably

s scenario. But note that she might have been able to, if the flop had been king high instead of q

gh (we can always to a separate analysis if we want to look further into this).

2 Defense against c-bets with a medium 10% flatting range


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is scenario was discussed in Part 1, and we only include the results here:

e remaining number of combos in Bob's range is 120:

timal 57% defense with 0.57 x 120 =68 combos:

Value raise:

{TT,55,QTs,AQ,AJ,KJ} =23 combos

Flat:

{KQ,QJs,JJ,ATs} =24 combos

Bluff raise:

{KTs,JTs,T9s,KJ,KJ,KJ,98,AJ,AJ,AJ,AJ,AJ,AJ,98,98,98} =22 combos


n-optimal defense under weak-tight restrictions:

Value raise:

{TT,55,QTs,AQ,AJ,KJ} =23 combos

Flat:

{KQ,QJs,JJ,ATs,KTs,JTs,T9s,98,KJs,AJ,AJ,AJ,AJ,AJ,AJ} =43 combos

Bluff raise:

None


b can easily get to optimal defense with his 10% flatting range on our coordinated example flo

ice can't c-bet any two cards profitably in this scenario either.

3 Defense against c-bets with a loose 15% flatting range


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e number of remaining combos in Bob's 15% flatting range is 174:

timal 57% defense means Bob has to defend 0.57 x 120 =99 combos. Here is one way to do it

Value raise:

{TT,55,QTs,AQ,AJ,KJ,J9} =24 combos

Flat:

{KQ,QJs,Q9s,JJ,AT,KTs,A9,A8,A7,A6,98,97,87,76,65} =48 combos

Bluff raise:

{JTs,T9s,KJ,KJ,KJ,J9,J9,J9,AJ (not AJ)} =27 combos


still easy for Bob to defend optimally on the coordinated flop, even with a loose preflop flatt

nge. His range is dominated by suited and coordinated high card hands, and it hits this type of f

ry hard. He has more than enough strong/medium hands and draws to use.

hen Bob is given weak-tight restrictions, defending enough will be harder. Mainly because he n

es the option to bluff raise, which is an important component of the defense on coordinated flo

w he has to call more, but it might be difficult for him to come up with enough flatting hands, s

can't use naked overcard/gutshot draws or his lowest pairs.

re is one way to defend under weak-tight restrictions:

Value raise:

{TT,55,QTs,AQ,AJ,KJ,J9} =24 combos

Flat:

{KQ,QJs,Q9s,JJ,AT,KTs,JTs,T9s,T8s,A9,A8,A7,A6,98,97,87,76,65,KJ,KJ,KJ,JS9,J9,J9,

(not AJ)} =72 combos

Bluff raise:

None



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b can get to optimal defense is he is willing to call the c-bet with all pairs 2nd pair or better,

ll as AJ for a overcard + gutshot draw. Alice still can't c-bet any two cards profitably on our

ordinated example flop.

. C-betting on dry flop

w we build Bob's defense strategies on the dry example flop from Part 1. For each range we f

ild his optimal strategy. On dry flops, Bob's defense consists of

latting with all his defense hands

e reason for using a flatting-only strategy on dry flop textures has been thoroughly discussed in

icle series "Optimal Postflop Play in NLHE 6-max". When the optimal strategies have been fo

impose the weak tight restrictions:





ising is not an option on dry flops regardless, so the restrictions only concern the hands Bob is

lling to flat with on the flop.

1 Defense against c-bets with a tight 5% flatting range

b has 62 remaining combos in his 5% flatting range after accounting for card removal effects_


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timal defense means defending 57% of these, which is 0.57 x 62 =35 combos. Here is one wa

it:

Value raise:

None

Flat:

{99,KQs,JJ-TT,88-66} =36 combos

Bluff raise:

None


b can easily get to optimal defense with his tight 5% range, without having to float with naked

ercards. Then we impose the weak-tight restrictions and see how that changes things. Now Bo

n't flat naked overcards, naked gutshots or pairs lower than the 9 on the board. This makes it

possible for Bob to defend enough. If he goes as far as he possibly can, he ends up with:

Value raise:

None

Flat:

{99,KQs,JJ-TT} =18 combos

Bluff raise:

None


b's problem in this scenario is that he is not willing to flat his lowest pairs and best overcards

Q). When he folds these hands, he can only get to about 1/2 of the necessary defense. He defen

ly 18/62 =29% of his range (as opposed to the optimal 57%), and folds 100 - 29 =71%. Alice

w exploit him by c-betting any two cards.

ice's EV for a pure c-bet bluff that can never win unless Bob folds on the flop is:


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(c-bet)

71 (P) + 0.29 (-0.75P)

0.49P

here P is the pot size on the flop. If the preflop raise was 3.5 bb, the pot is P =2(3.5) + 0.5 + 1

The EV of Alice's c-bet bluff is then 0.49 x 8.5 bb =4.2 bb.

te that when Bob's preflop flatting range is tight, our conclusions are very dependent on the ex

ds that come on the flop, as well as the exact hands Bob's range is made up of. For example, ib had elected to flat the 12 KQo combos instead of the 12 66/55 combos, he would have been

defend about optimally on this king high flop texture, also with the restricted strategy.

hen Bob's range is very tight, we can gain a lot from paying close attention. Some players flat a

rs, others fold or 3-bet-bluff the lowest pairs and flat more Broadway hands instead. Observe

nds that go to showdown, and take notes. If your PokerTracker/HEM database has many hands

yer, you can use it to extract information and take notes between sessions (this is a smart thing

for opponents you meet regularly).

2 Defense against c-betting with a medium 10% flatting range

is work was done in Part 1, and below is a summary of the results:

e number of combos after card removal is 126:

b defends 0.57 x 126 =72 combos when playing optimally. Here is one way to do it:

Value raise:

None

Flat:

{99,22,KQ,KJs,KTs,JJ-TT,T9s,98s,88-66,AQ} =76 combos

Bluff-raise:

None



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d here is one way Bob can defend under the weak-tight restrictions:

Value raise:

None

Flat:

{99,22,KQ,KJs,KTs,JJ-TT,T9s,98s} =42 combos

Bluff-raise:None


b now defends only 42/126 =33% of his range and folds 100 - 33 =67%. Alice can exploit thi

bet bluffing any two cards. Her EV for a c-bet bluff with a worthless hand is:

(c-bet)

67 (P) + 0.33 (-0.75P)

0.42P

here P is the pot size on the flop. With a pot of 8.5 bb, the EV is 0.42 x 8.5 bb =3.6 bb.

3 Defense against c-betting with a loose 15% flatting range

e'll see that this is a difficult job for Bob when we impose weak-tight restrictions. The numbermbos that remain in his range after accounting for card removal effects is 180:

timal 57% defense means Bob has to use 0.57 x 180 =103 combos. Here is one way to do it:

Value raise:

None

Flat:

{99,22,K9s,KQ,KJs-KTs,JJ,TT,A9s,Q9s,J9s,T9s,98s-97s,88-55,AQ,QJs,JTs} =104 comb

Bluff raise:

None


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b has to flat almost all of his pairs, plus some overcard hands (AQ) and gutshots (QJs, JTs). I

rd enough to defend optimally when Bob can use all hands, and when we impose weak-tight

trictions, it becomes impossible. Here is what Bob comes up with when he goes as far as he c

Value raise:None

Flat:

{99,22,K9s,KQ,KJs-KTs,JJ,TT,A9s,Q9s,J9s,T9s,98s-97s} =56 combos

Bluff-raise:

None


e defense is more or less identical to the optimal defense, except that we have dropped all pai

wer than 9, all naked overcard hands (AQ) and all naked gutshots (QJs, JTs). Bob now defend

out 1/2 of the optimal amount: 56/180 =31% of his range. So he folds 100 - 31 =69% on the fl

d the EV for Alices' c-bet bluffs becomes:

(c-bet)

69 (P) + 0.31 (-0.75P)

0.46P

here P is the pot size on the flop. With P =8.5 bb, the EV becomes 0.46 x 8.5 bb =3.9 bb.

a c-bet bluff will be automatically profitable on the flop, but note something else as well: Bob

ced to defend on the flop with many low pairs and weak draws, also under weak-tight restrict

Alice should have many opportunities to 2-barrel profitably on the turn. Bob can protect hims

mewhat against 2-barrel bluffs by slowplaying his strongest hands on the flop, but life will stil

ugh for him on the turn if Alice decides to bluff a lot.

a good player with knowledge about Bob's preflop flatting range and his postflop tendencies

ould be able to make even more money from c-bet bluffing by sometimes continuing to bluff on

n and the river. But note that we don't have to continue out bluffs in order to have a nicely

ofitable c-bet bluff in isolation on the flop.

. Summary


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e used the two example flop textures (very coordinated and very dry) from Part 1 and continue

odeling of c-bet bluffing. This time we let Bob use 3 preflop flatting ranges:

A tight 5% range

A medium 10% range (our standard "IP flat list")

A loose 15% range

sed on our modeling, we conclude the following:

We can't c-bet bluff profitably with any two cards on a very coordinated flop against any

reasonable flatting range, even if our opponent defends weak-tight

On very dry flops we can c-bet bluff profitably with any two cards, if our opponent defend

weak-tight

e noted that the profitability of a c-bet bluff against the tight 5% range on a dry flop was verynsitive to the exact flop texture and the exact composition of the flatting range. At the other end

spectrum, this became relatively unimportant against the loose 15% range.

wide and weak preflop flatting range is impossible to defend correctly against c-bets on a very

p, unless the player is willing to flat just about any pair plus lots of overcard and gutshot comb

actly what the flop is, and exactly which hands we flat is now less important, since we have to

fend lots of weak hands/draws regardless.

e summarize:

very coordinated flops we can't get away with any two cards c-bet bluffing regardless of o

ponents preflop flatting range. If he defends weak-tight, this does not help you a lot, since v

ordinated flop textures are so easy to defend.

very dry flops you can probably get away with any two cards c-bet bluffing regardless of y

ponent's flatting range, as long as he isn't willing to always defend optimally. A wide flattin

nge gives you the best opportunities, since wide ranges are very hard to defend optimally onry dry flops. Of course, against an opponent that always defends optimally, we can't buff an

o cards profitably, per definition. But most players are unable or unwilling to defend enoug

y flops. So our starting assumption can be that any-two-cards c-bet bluffing is profitable on

y flops. If we are wrong against a particular opponent, we can adjust later, and start check

re hands.

Part 3 we'll look at some other flop textures in the region between very coordinated and very d

ps. We'll also introduce a software tool ("Flopzilla") that lets us quickly analyze the profitabi

a c-bet bluff, without having to write out complete strategies like we have done up to this poin
http://www.cardrunners-ev-calculator.com/Flopzilla.html


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Optimal flop cbetting - part 2

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